Question

could someone explain this to me in an easy way to understand. Thank you kindly.


Point out that to graph the function
f (x) = a (x - h)^ 3+ k, you identify the point of
symmetry (h, k) and use the value of a to draw the
graph through two additional points
(-1 + h, –a + k) and (1 + h, a + k). So, to graph
f (x) = 2 (x - 3) ^3+ 1, first identify the point of
symmetry, (3, 1). Then identify points
(-1 + 3, -2 + 1) = (2, -1) , and
(1 + 3, 2 + 1) = (4, 3) as additional reference points.
A smooth curve through these three points is a good
beginning for the graph.

Answer 1

looks good to me

Answer 2

I mean, consider the graph of x^3
stretch it up by a factor of 2
shift it right by h and up by k
Since (-1,-1), (0,0), and (1,1) lie on the graph of x^3,
(-1+h,-a+k), (h,k), and (1+h,a+k) lie on the graph of f(x)